Internal problem ID [13120]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 8. Review exercises for part of part II. page 143
Problem number: 18.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]
\[ \boxed {y^{\prime }-\frac {3 y}{x +1}+y^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 42
dsolve(diff(y(x),x)=3*y(x)/(1+x)-y(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {4 x^{3}+12 x^{2}+12 x +4}{x^{4}+4 x^{3}+6 x^{2}+4 c_{1} +4 x +1} \]
✓ Solution by Mathematica
Time used: 0.258 (sec). Leaf size: 41
DSolve[y'[x]==3*y[x]/(1+x)-y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {4 (x+1)^3}{x^4+4 x^3+6 x^2+4 x+1+4 c_1} y(x)\to 0 \end{align*}